FINANCIAL APPLICATIONS OF STABLE DISTRIBUTIONS: IMPLICATIONS ON TURKISH STOCK MARKET

Year 2017, , 364 - 374, 30.12.2017

Hulya Basegmez Elif Cekici

https://doi.org/10.17261/Pressacademia.2017.769

Abstract

Purpose- The aim of this study is modelled by examining the trading
volumes of the tourism companies located in the high-risk tourism sector and
traded in BIST. This modelling will gain point of view for the tourism firms as
well as make an important contribution to the decision making of investors who
want to invest in this sector.

Methodology- The study is
conducted for a sample of 2803 daily trading volumes over the period
01.01.2007-28.09.2017. Then, it is used daily returns rather than daily trading
volume data because it provides the ability to measure investment performance
independently of the scale used.  Daily
return data is modelled with stable distributions used with increasing interest
in many application areas and that are well-suited to financial asset returns.
Parameter estimates is made by using quantiles method which is one of the most
known estimation methods. 

Findings-  By means of
the Chi-square test and graphs, it is seen that normal distribution was not
suitable for trading volume data. Stable distribution parameters for the
log-returns data are estimated according to the quantiles method and obtained
the stable parameters 𝛼, 𝛽, 𝛾  and 𝛿.  Stable density function is obtained using the
MATLAB STBL command according to estimated parameters.

Conclusion- Estimated parameter values indicate that stable
distributions can be used as a suitable model for modelling the transaction
volume data of analysed index.  It has been concluded that it is more
appropriate to use the scale parameter of the stable distribution instead of
the standard deviation as the risk measure.

Keywords

BIST Tourism, stable distributions, parameter estimation

References

• Barndorff-Nielsen, Ole E., Thomas Mikosch, and Sidney I. Resnick, eds., 2012. “Lévy processes: theory and applications.” Springer Science & Business Media.
• Borak, Szymon, Wolfgang Härdle, And Rafał Weron, 2005. "Stable Distributions." Statistical Tools For Finance and Insurance. Springer, Berlin, Heidelberg, 21-44.
• Çekici, E., 2003. “İşlem Hacmi Verilerinin Kararlı Paretian Dağılımlarla Modellenmesi”, PhD Thesis, Marmara University, Istanbul, Turkey.
• Fama, Eugene F., 1965. "The behavior of stock-market prices." The journal of Business 38.1, 34-105.
• Fama, Eugene F., and Richard Roll, 1968. "Some properties of symmetric stable distributions." Journal of the American Statistical Association 63.323, 817-836.
• Fama, Eugene F., and Richard Roll, 1971. "Parameter estimates for symmetric stable distributions." Journal of the American Statistical Association 66.334, 331-338.
• Fan, Zhaozhi, 2006. “Parameter Estimation of Stable Distributions.” Communications in Statistics - Theory and Methods, 35.2, 245-255.
• Hill, Bruce M., 1975. "A simple general approach to inference about the tail of a distribution." The annals of statistics 3.5, 1163-1174.
• Inskeep, Edward, 1991. “Tourism planning: an integrated and sustainable development approach.” Van Nostrand Reinhold.
• Kateregga, M., Mataramvura, S. and Taylor, D., 2017. "Parameter estimation for stable distributions with application to commodity futures log-returns." Cogent Economics & Finance 5.1, 1318813.
• Kuruoglu, Ercan E., 2001. "Density parameter estimation of skewed 𝛼-stable distributions." IEEE transactions on signal processing 49.10, 2192-2201.
• Mandelbrot, Benoit, 1963. "The variation of certain speculative prices." The World Scientific Handbook of Futures Markets. 39-78.
• McCulloch, J. Huston, 1986. "Simple consistent estimators of stable distribution parameters." Communications in Statistics-Simulation and Computation 15.4, 1109-1136.
• Nolan, John P., 1998. “Parameterizations and modes of stable distributions.” Statistics & probability letters 38.2, 187-195.
• Nolan, John P., 2001. “Maximum likelihood estimation and diagnostics for stable distributions.” Lévy processes: theory and applications, 379-400.
• Nolan, John, 2016. “Stable distributions: models for heavy-tailed data.” New York: Birkhauser, http://academic2.american.edu/~jpnolan/stable/chap1.pdf
• Önalan, Ö., 2010. “α− Kararlı Dağılımlarla Finansal Risk Ölçümü.” 28(1), 549-571.
• Özdemir, M. A., and Kervankıran, İ., 2013. “Determining the Attitudes of Local People Towards Tourism and Its Effects: A Case Study From Afyonkarahisar.” , Marmara Geographical Review 24, 1-25.
• Uchaikin, V. V., & Zolotarev, V. M., 1999. “Chance and stability: stable distributions and their applications.” Walter de Gruyter.
• Veillette, Mark, 2012. "STBL: Alpha stable distributions for MATLAB." Matlab Central File Exchange, retreived November 10. http://www.mathworks.com/matlabcentral/fileexchange/37514-stbl--alpha-stable-distributions-for-matlab/content/STBL_CODE/stblrnd. m>. Acesso em, 11, 46.
• Yang, Yiyang, 2012. "Option pricing with Non-Gaussian Distribution-Numerical Approach."
• Zolotarev, Vladimir M., 1996. “One-dimensional stable distributions.” American Mathematical Soc., Vol. 65.